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We developed a three-center phenomenological model,able to explain qualitatively the recently obtained experimental results concerning the quasimolecular stage of a light-particle accompanied fission process. It was derived from the liquid drop model under the assumption that the aligned configuration, with the emitted particle between the light and heavy fragment, is reached by increasing continuously the separation distance, while the radii of the heavy fragment and of the light particle are kept constant. In such a way,a new minimum of a short-lived molecular state appears in the deformation energy at a separation distance very close to the touching point. This minimum allows the existence of a short-lived quasi-molecular state, decaying into the three final fragments.The influence of the shell effects is discussed. The half-lives of some quasimolecular states which could be formed in the $^{10}$Be and $^{12}$C accompanied fission of $^{252}$Cf are roughly estimated to be the order of 1 ns, and 1 ms, respectively.